Maths

posted by .

A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.

  • Maths -

    Let the river flow in the +x direction.
    Across the river is then +y.

    river velocity = (20,0)
    boat velocity relative to the water
    = (20cos70°,20sin70°) = (6.84,18.79)

    resultant velocity relative to land
    = (26.84,18.79)

    speed: √(26.8^2+18.79^2) = 32.73
    direction:
    tanθ = y/x = 18.79/26.84 = .70
    θ = 35°

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Math: Calculus - Vectors

    A boat travels at a speed of 5 m/s in still water. The boat moves directly across a river that is 70m wide. The water in the river flows at a speed of 2 m/s. How long does it take the boat to cross the river?
  2. Physics

    A motorboat heads due east at 8.5 m/s across a river that flows to the south at a speed of 2.5 m/s. a. What is the velocity of the boat relative to a stationary observer on the shore?
  3. Physics

    A river is flowing 4.0 m/s to the east. A boater on the south shore plans to reach a dock on the north shore 30.0 Degrees downriver by heading directly across the river. What should be the boat's speed relative to the water?
  4. Physics

    A river is flowing 4.0 m/s to the east. A boater on the south shore plans to reach a dock on the north shore 30.0 Degrees downriver by heading directly across the river. What should be the boat's speed relative to the water?
  5. physics

    A river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 9.2 m/s due north relative to the water. (a) What is the velocity of the boat as viewed by an …
  6. Physics

    A boat crosses a river of width 113 m in which the current has a uniform speed of 0.933 m/s. The pilot maintains a bearing (i.e., the direction in which the boat points) perpendicular to the river and a throttle setting to give a constant …
  7. Pre calculus, vectors

    A straight river flows at a speed of 20km/h. A boater starts at the south shore and heads in ths direction of 70degrees from the shore. The boat has a speed of 20km/h in still water. Find the true speed and direction of the boat.
  8. physics

    a river flows due east at 1.50 m/s. A boat crosses the river from the south shore to the north shore by maintaining a constant velocity of 10m/s due north relative to the water. (a) what is the velocity of the boat relative to the …
  9. Physics

    a boat crosses a 2 km wide river by starting out at the south shore and heading directly for the north shore if the river flows at 0.8 m/s and the boat can go at 1.4 m/s in still water, where on the opposite shore will the boat land?
  10. Physics

    a boat crosses a 2 km wide river by starting out at the south shore and heading directly for the north shore if the river flows at 0.8 m/s and the boat can go at 1.4 m/s in still water, where on the opposite shore will the boat land?

More Similar Questions